Sam Allardyce's side finished 10th last season in their first year back in the top flight after earning promotion via the Championship play-offs.
Diame played a key role for the Hammers throughout the campaign following his free transfer move from Wigan Athletic last summer.
After being given extra time off due to his international commitments, Diame got his first taste of action ahead of the 2013/14 season in Saturday's 2-0 friendly win over Bournemouth.
The 26-year-old feels the Upton Park outfit can build on their solid display last time out and push for a place in the upper reaches of the Premier League this term.
"We have to have our ambition and we know the project of the club. We need to work to try to finish near the top," he told the club's official website.
"We are going to try to give our best and make sure we do better than the last season. I feel a top-eight finish is achievable, of course. Why not?
"I see everybody is focused to be in the starting XI. Everybody is working hard so this is good for the team.
"We just need to be focused on the first game against Cardiff because we know it is important to start well to make the season easier."